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The Metric System
In ancient times, there was confusion about how to measure
things.
When people tried to measure using the parts of their body they discovered that
people aren’t built the same. Not everyone has the same foot size, arm size, hand size,
etc.
To measure weight people tried using stones.
But what problem does this pose?
Stones come in different sizes.
And the same confusion arose when trying to find the volume of a container.
How many seeds does this container hold?
Again, it depends on the size of the seed.
Eventually people began to use the same ruler. Now a foot was a foot whether you lived in Eastonesia or
Westlovakia.
Above is a sample of the ruler we use today in the US, we use units like inches, feet, yards and miles for measuring length and distance.
To measure weight people started using a system of pounds, ounces,
and tons
and for Volume… Cups, Pints, Quarts and Gallons were used.
But this system, called the Customary System, was still
confusing (to everyone but the United States)
Because we are one of the only countries to still use the
Customary System of Measurement.
So if the United States is the only country still using the Customary
System to measure, what is everybody else using?
THE METRIC SYSTEMaka The International System of Units (SI)
• The metric system is based on a base unit that corresponds to a certain kind of measurement
• Length = meter
• Volume = liter
• Mass = gram
• Prefixes plus base units make up the metric system – Example:
• Centi + meter = Centimeter• Kilo + liter = Kiloliter
Metric System
• The three prefixes that we will use the most are:– Kilo (means 1000)– centi (means 1/100)– milli (means 1/1000)
kilo hecto deca
Base Units
meter
gram
liter
deci centi milli
Let me try to clear this up with a table:
Measuring Distances and Lengths Using the Metric System
Small Distances/Lengths
Standard Distances/Lengths
Larger Distances/Lengths
Millimeters (mm)
Centimeters (cm)
Meter (m)Kilometers (km)
Mili- means 1
1000
Kilo- means 1000
Let’s look at a Meter Stick
The space marked off is equal to 1 cm
This tiny space marked off is 1 mm
The height of our door is
about 2 meters.
So let’s add to our notes:
100 cm = 1 m
1,000 mm = 1 m
1,000 m = 1 km
Measuring Volume Using the Metric System
Small Volumes Standard Volumes
Larger Volumes
Milliliters (mL)Liter (L)
Kiloliter (kL)
1000 mL = 1 L
1000 L = 1 kL
Mili- means 1
1000
Kilo- means 1000
Measuring Mass Using the Metric System
Small Mass Standard Mass Larger Mass
Milligrams (mg)Gram (g)
Kilograms (kg)1000 mg = 1 g
1000 g = 1 kg
Mili- means 1
1000
Kilo- means 1000
Since there are currently two systems of measuring this can add
to the confusion…And sometimes misunderstandings about
measurements can lead to DISASTER!
The engineers and operators who worked on a multimillion dollar spacecraft made such a mistake. Some of them used feet and miles, while others used meters and kilometers…After blastoff the spacecraft
was supposed to orbit Mars, but instead it was lost in space forever.
However, even though the metric system has not been adopted by
people in the US, most Americans use it everyday.
Check your refrigerators, pantries, medicine cabinets and bathrooms.
Measured in grams
Measured in milligrams
Measured in milliliters
Many manufacturers use metric units because they are understood
all over the world.
• What if you need to measure a longer distance, like from your house to school?– Let’s say you live approximately 10 miles
from school• 10 miles = 16093 meters
– 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage:
• 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)
Metric System• These prefixes are based on powers of 10.
What does this mean?– From each prefix every “step” is either:
• 10 times larger or
• 10 times smaller
– For example• Centimeters are 10 times larger than millimeters• 1 centimeter = 10 millimeters
kilo hecto deca
Base Units
meter
gram
liter
deci centi milli
Metric System
– Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length
1 centimeter = 10 millimeters
Example not to scale
1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm
1 cm
40
41
41
40
Metric System• For each “step” to right,
you are multiplying by 10
• For example, let’s go from a base unit to centi
1 liter = 10 deciliters = 100 centiliters
2 grams = 20 decigrams = 200 centigrams
kilo hecto deca
meter
liter
gram
deci centi milli
( 1 x 10 = 10) = (10 x 10 = 100)
(2 x 10 = 20) = (20 x 10 = 200)
Metric System• An easy way to move within the metric system is
by moving the decimal point one place for each “step” desired
Example: change meters to centimeters
1 meter = 10 decimeters = 100 centimetersor
1.00 meter = 10.0 decimeters = 100. centimeters
kilo hecto deca
meter
liter
gram
deci centi milli
Metric System• Now let’s try our previous example from meters to
kilometers:
16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers
• So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)
kilo hecto deca
meter
liter
gram
deci centi milli
Metric System
• If you move to the left in the diagram, move the decimal to the left
• If you move to the right in the diagram, move the decimal to the right
kilo hecto deca
meter
liter
gram
deci centi milli
• PRACTICE PROBLEMS
Metric System• Now let’s start from meters and convert to centimeters
5 meters = 500 centimeters
kilo hecto deca
meter
liter
gram
deci centi milli
kilo hecto deca
meter
liter
gram
deci centi milli
• Now let’s start from kilometers and convert to meters
.3 kilometers = 300 meters